Triple positive solutions for a class of third-order p-Laplacian singular boundary value problems

In this work, we study the existence of triple positive solutions for one-dimensional p-Laplacian singular boundary value problems lφp(y″(t)))′+f(t)g(t,,y(t),,y′(t),, y″(t))=0,quad 0<t<1,\[3pt ay(0)-by′(0)=0, cy(1)+dy″(1)=0, y″(0)=0, where φ p (s)=|s| p-2 s,∈p>1, g:[0,∈1 ×[0,∈+∞)×R 2[0,∈+∞) and f:(0,∈1)[0,∈+∞) are continuous. The nonlinear term f may be singular at t=0 and/or t=1. Firstly, Green's function for the associated linear boundary value problem is constructed. Then, by making use of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the above boundary value problem. The interesting point is that the nonlinear term g involved with the first-order and second-order derivatives explicitly. © 2010 Korean Society for Computational and Applied Mathematics.